Let flay) = sinbet). ComPAe Dufy) wlere V= (83)

Q: - 5. Consider th gonal to vector (-

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Q: orthogonal

A: We have   u=111    and v=2-12 are two column matrices  . We have to find the value of  k so that…

Q: Show that a fomws with R>o Ssee igue] may be descuibed panometuicaly by u cU,N] Cosu, (R+ o…

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Q: Find diagonal matriy D is similar with A a A = [3 8-5

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Q: Theorem 8o4 ŏ In a parallileguam, oppesitiangles ale equal aie

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Q: The projection of u onto v is given by projvu = ________.

A: The projection of u onto v is given by projvu = compvu.

Q: cosulen Dhe probubily densty functren OTherwise which randen werclde Xfellews Find pobebility Tht

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Q: 7. Show for y = u.v that y"= uv"' + 3u' v'" + 3u" v' + u''' v.

A: The detailed solution is as follows below:

Q: cond, and third prizes be drawn from a box containing 120 names?

A: A box containing 120 names 3 prizes be drawn

Q: A, is skew-symmetric, then prove that (B B + B, B') An = . Ajk = 0. %3D

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Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: Let = (0,- 2)v=(3,2) and w=(-2,1) Then the dot product u. (V w) is equal to

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Q: find the fimet Qurtal dernratives 7 respect to rarraes X,4,Z.

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Q: A Bystem is defined by %3D () betermine the cortro Uability and oboervabitity of the bystem

A: NOTE : As per Bartleby portal , incase of multiple subparts only first three are answered. Please…

Q: Compute Cov(X,Y)

A: Solution: From the given information, the joint distribution is

Q: If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g…

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Q: An electromagnetic wave does require a medium to travel. O True O False

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Q: 16. Write a two column proof. Given: OSTUV U V. Prove: AVXS = AUXT T S 8.

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Q: Suppose e vectors. that a and b ave nonzero Under what ciraumstarces is comp= compas Under ahat…

A: According to the problem, we have

Q: (b) Compute r if: arctan r + arctan 1 = 2 ( arctan z arctan

A: tan-1x+tan-11=2tan-1x-tan-113

Q: use Parsevol's theoverm to find u if fit)-Ae'

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Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

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Q: 16. Obtain the toigonometric fouries seajes for A fit) > wt 277

A: The given image is of sine wave form. Here, period T=πand so, w0=2πT=2ππ=π

Q: et X~U([-, 1) and let y = tan(r), show that y Cauchy(0, 1)

A: # using Jacobian transformation we have proved that y=tanx follow Cauchy distribution (0, 1)

Q: Prove that MSE(Ô) = V (ô) + [Bias(Ô)]²

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Q: 2.Prove that I (sinwt) : s2+w?

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Q: 5. Use De Moivre's Theorem to evaluate (1 – V3i)%.

A: Demoivre's Theorem

Q: Show using MGF technique that if Z, - N(0,1), for i = 1,2,3,4,5 , then U = Ez - x² with 5 degrees of…

A: Using the MGF technique we have to prove that : U = ∑i=15Z2i ~ χ2 with 5 degrees of freedom, If Zi ~…

Q: Q: Prove that tim x"- a" %3D

A: we have to find the limit of the expression

Q: Find and when (TU – V)² In(W – UV) = In(2) at the point (T, U, V, W) = (1, 1, 2, 4).

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Q: The angle between (0, –6, 2) and (4, 8, 7) is: O A. orthogonal - O B. acute.

A: We will use geometric definition to determine the angle.

Q: SHOW that V Ź a? Jor a, E IR when His ineguaity e kold .

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Q: Region ¥=1=sino jn 1-st q4adrant enclosed by the eardieid

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Q: When using Simpson's rule we must having two distinct point Select one: True False

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Q: dual of c, is isometric to l'.

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Q: Let f lany) prove that' flany) di f feren tiable I5 not point lo,0) .

A: Let the function be fx,y=xy Note:  [ We can say that f is differentiable at (a,b) if f is…

Q: ху • prove that x +y Example If z = az dz + y.- Əx х. ду

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Q: Find the maaimum and miniryem Valiaes of e feencteon Cif exits) feny) Luž-3ary

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Q: Find first and second fundamenta! Texm U-V e Cos 2sin U-V of

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Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: 2. is it or divery Con

A: To solve the problem and find its convergence

Q: Suppose u, VE Vand ||u|| < 1 and ||v|| < 1 . Prove it: V1- ||u||?/1- ||u||2 <1- (u, v)|

A: Suppose u, v∈V and u≤1 and v≤1 We have to prove that 1-u21-v2≤1-u,v Here, we have  u≤1 and v≤1 Also,…

Q: (X), E(Y ) EXY), Cov(X, Y) , σχ, σχ and Py.

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Q: Find a non zero unit vecor ô that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: We have to find a non-zero vector V that is orthogonal to u1=1,2,1 and u2=2,5,4 in R3.

Q: Which part (Given or Prove) of the proof depends upon the a) hypothesis of theorem? b) conclusion of…

A: (a) Hypothesis of the theorem :             The hypothesis of the theorem is been used for the…

Q: 3 tari' (xty) , Prane that x2+ ydz Sen 2z be

A: We have z=tan-1x+yx-y This implies tanz=x+yx-y Let u=tanz Then we first need to find the degree of…

Q: Explain the fundamental theorem of albenra?

A: To explain: Fundamental theorem of Algebra